In the generalized orbifold case, or more generally the case of smooth projective Deligne-Mumford stacks, the GW theory has been studied in [[1]}, [2]}]. A degeneration formula of this orbifold GW theory is obtained in [[3]}] by using the notion of stacks of twisted expanded degenerations and pairs in [[4]}] which generalizes the original one defined by Jun Li [[5]}]. Without the twisted condition, the author in [[6]}] directly generalizes Jun Li's stacks of expanded degenerations and pairs to the case of smooth projective Deligne-Mumford stacks, which leads to the construction of good degenerations of Hilbert stacks generalizing the one in [[7]}]. In [[6]}], the author also gives the definition of the absolute and relative orbifold DT theory (see also [[9]}, [10]}] for the prior definition with Calabi-Yau condition) and derives the corresponding degeneration formulas. In [[11]}], the author constructs moduli spaces of orbifold PT stable pairs and defines virtual fundamental classes which are integrated to give the absolute orbifold PT invariants for 3-dimensional smooth projective Deligne-Mumford stacks (see also [[12]}] for the prior definition in the case of Calabi-Yau 3-orbifolds). However, it is naturally expected to have the relative orbifold PT theory and the corresponding degeneration formula.
